Answer
$T=\pi \sqrt{\frac{2L(m_1+m_2)}{g(m_1-m_2)}}$
Work Step by Step
We can find the required time period as follows:
$T=2\pi (\frac{l}{g})(\frac{I}{ml^2})$
$\implies T=2\pi (\sqrt{\frac{L(m_1-m_2)}{2g(m_1+m_2)}})(\frac{m_1+m_2}{m_1-m_2})$
This simplifies to:
$\implies T=\pi \sqrt{\frac{2L(m_1+m_2)}{g(m_1-m_2)}}$
